Data from under-researched languages are now available in sufficient quantity and quality to feed into corpus-based approaches to language typology. In this paper we present Multi-CAST (Multilingual Corpus of Annotated Spoken Texts), a project designed to facilitate cross-linguistic comparison of naturalistic discourse across typologically diverse languages, which implements a purpose-built shared annotation scheme. After sketching the rationale and architecture of Multi-CAST, we illustrate the efficacy of the method with two case-studies: The first one investigates the rates of lexical (as opposed to pronominal and zero) realization of arguments in discourse across a sample of 15 typologically diverse languages. Our results reveal a remarkable and hitherto unnoticed uniformity in the density of lexical references, despite the lack of content control in the corpora. The second addresses the question of whether cross-linguistically attested regularities in morphosyntax can meaningfully be related to frequency effects in discourse. We find some support for frequency-based explanations, but our data also show that the frequency accounts leave several key questions unanswered. Overall, our findings underscore that research based on language documentation-derived corpus data, and in particular spoken language data, is not only possible, but in fact crucially necessary for testing frequency-based explanations, because these data stem from spoken language and typologically diverse languages. We also identify a number of epistemological and methodological shortcomings with our approach, and discuss some of the requirements for further innovation in areas of corpus building, corpus annotation, and typological comparability.